Order of Operations (C) worksheet with six math problems to simplify using the correct order of operations.

Let's solve each expression step by step using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

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Problem 1:

$$
(4^2 - 7 + (-9))^3 \div (2 \times 8)
$$

Step 1: Evaluate exponents and parentheses.

- $4^2 = 16$
- So inside the parentheses: $16 - 7 + (-9) = 9 - 9 = 0$
- Now: $(0)^3 = 0$
- Denominator: $2 \times 8 = 16$

Now divide:
$$
0 \div 16 = 0
$$

✔ Answer: 0

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Problem 2:

$$
((-2) - 2^2) \times ((-3) + (-5)) \div ((-9) + 6)
$$

Step 1: Exponents first.

- $2^2 = 4$
- So: $(-2) - 4 = -6$

Next: $(-3) + (-5) = -8$

Then: $(-9) + 6 = -3$

Now substitute:
$$
(-6) \times (-8) \div (-3)
$$

Step 2: Multiplication and division from left to right.

- $(-6) \times (-8) = 48$
- $48 \div (-3) = -16$

✔ Answer: -16

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Problem 3:

$$
(10 \div ((-7) - (-8))) \times (-10) + 8^2 + (-5)
$$

Step 1: Simplify inside innermost parentheses.

- $(-7) - (-8) = -7 + 8 = 1$
- So: $10 \div 1 = 10$

Now:
$$
10 \times (-10) + 8^2 + (-5)
$$

Step 2: Exponent: $8^2 = 64$

Now:
$$
10 \times (-10) = -100
$$

Now add:
$$
-100 + 64 + (-5) = -100 + 64 - 5 = -41
$$

✔ Answer: -41

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Problem 4:

$$
((-9) + 9) \times 3 \div (8 - 5)^3 \div 4
$$

Step 1: Simplify parentheses.

- $(-9) + 9 = 0$
- $8 - 5 = 3$, so $3^3 = 27$

Now:
$$
0 \times 3 \div 27 \div 4
$$

Any number multiplied by 0 is 0:
$$
0 \div 27 \div 4 = 0
$$

✔ Answer: 0

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Problem 5:

$$
(6 + (-5)) \div (8 - 7) \times (-3) + (-9)^2
$$

Step 1: Simplify parentheses.

- $6 + (-5) = 1$
- $8 - 7 = 1$

So:
$$
1 \div 1 \times (-3) + (-9)^2
$$

Step 2: Exponent: $(-9)^2 = 81$

Now do division and multiplication left to right:

- $1 \div 1 = 1$
- $1 \times (-3) = -3$

Now add:
$$
-3 + 81 = 78
$$

✔ Answer: 78

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Problem 6:

$$
((-6) \times (10 - 2 + (-8))^3) \div 8^2
$$

Step 1: Simplify inside parentheses.

- $10 - 2 + (-8) = 8 - 8 = 0$
- So: $(0)^3 = 0$

Now:
$$
(-6) \times 0 = 0
$$

Then divide by $8^2 = 64$:
$$
0 \div 64 = 0
$$

✔ Answer: 0

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✔ Final Answers:

1. $0$
2. $-16$
3. $-41$
4. $0$
5. $78$
6. $0$

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